Abstract
We consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these singularities are a clear diagnostic of bulk locality. We analyze some properties of these perturbative singularities and discuss their relation to the OPE and the dimensions of double-trace operators. In the exact nonperturbative theory, we expect no singularity at these locations. We prove this statement in 1+1 dimensions by CFT methods.
Highlights
In Euclidean signature, correlators of local operators are analytic for non-coincident points
In theories that have gravity duals, singularities can arise from Landau diagrams in the bulk
We consider singularities arising from a local bulk. We argue that these singularities do not arise from boundary Landau diagrams in 1+1 and 2+1 dimensions
Summary
In Euclidean signature, correlators of local operators are analytic for non-coincident points. In Lorentzian signature, singularities can arise when “something happens.” These Lorentzian singularities correspond, in weakly coupled theories, to Landau diagrams consisting of a set of null particles interacting at local vertices in an energy-momentum conserving fashion. In theories that have gravity duals, singularities can arise from Landau diagrams in the bulk In some cases, these occur at positions where there is no Landau diagram on the boundary [9,10,11,12,13]. We argue that these singularities do not arise from boundary Landau diagrams in 1+1 and 2+1 dimensions. Other appendices give more details on the discussion in the main body
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